Airfoil shape for a compressor

ABSTRACT

An article of manufacture having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in TABLE A. X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches. The profile sections at the Z distances can be joined smoothly with one another to form a complete airfoil shape.

BACKGROUND OF THE INVENTION

The present invention relates to airfoils for a vane of a gas turbine.In particular, the invention relates to compressor airfoil profiles fora Stage 4 rotor vane.

In a gas turbine, many system requirements should be met at each stageof a gas turbine's flow path section to meet design goals. A turbine hotgas path requires that the compressor airfoil rotor vane meet designgoals and desired requirements of efficiency, reliability, and loading.For example, and in no way limiting of the invention, a vane of acompressor rotor should achieve thermal and mechanical operatingrequirements for that particular stage. Further, for example, and in noway limiting of the invention, a vane of a compressor rotor shouldachieve thermal and mechanical operating requirements for thatparticular stage.

Past efforts to meet design goals and desired requirements have providedcoatings on the airfoil, but the coatings may not be robust enough orpermanent to provide design goals and desired requirements. Accordingly,it is desirable to provide an airfoil configuration with a profile meetto design goals and desired requirements.

BRIEF DESCRIPTION OF THE INVENTION

In one embodiment of the invention, an article of manufacture comprisesa vane airfoil having an airfoil shape, the airfoil having a nominalprofile substantially in accordance with Cartesian coordinate values ofX, Y and Z set forth in TABLE A. X and Y are distances which, whenconnected by smooth continuing arcs, define airfoil profile sections ateach distance Z in inches. The profile sections at the Z distances arejoined smoothly with one another to form a complete airfoil shape.

In another embodiment according to the invention, a compressor vaneincludes a vane airfoil having an uncoated nominal airfoil profilesubstantially in accordance with Cartesian coordinate values of X, Y andZ set forth in TABLE A. X and Y are distances in inches which, whenconnected by smooth continuing arcs, define airfoil profile sections ateach Z distance in inches. The profile sections at the Z distances arejoined smoothly with one another to form a complete airfoil shape. X andY distances are scalable as a function of a constant to provide ascaled-up or scaled-down airfoil.

In a further embodiment of the invention, a compressor comprises acompressor wheel having a plurality of blades cooperating with rotorvanes. Each of the vanes includes an airfoil having an airfoil shape.The airfoil comprises a nominal profile substantially in accordance withCartesian coordinate values of X, Y and Z set forth in TABLE A. X and Yare distances in inches which, when connected by smooth continuing arcs,define the airfoil profile sections at each distance Z in inches. Theprofile sections at the Z distances are joined smoothly with one anotherto form a complete airfoil shape.

In a yet further embodiment of the invention, a compressor comprises acompressor wheel having a plurality of blades cooperating with rotorvanes, and each of the vanes include an airfoil having an uncoatednominal airfoil profile substantially in accordance with Cartesiancoordinate values of X, Y and Z set forth in TABLE A. X and Y aredistances which, when connected by smooth continuing arcs, defineairfoil profile sections at each distance Z in inches. The profilesections at the Z distances are joined smoothly with one another to forma complete airfoil shape. The X, Y and Z distances are scalable as afunction of a constant to provide a scaled-up or scaled-down vaneairfoil.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a fragmentary cross-sectional view of a compressorillustrating various stages of the compressor, as embodied by theinvention;

FIG. 2 is perspective view of a blade for a compressor, as embodied bythe invention;

FIG. 3 is a side elevational view thereof;

FIG. 4 is a tangential and rear perspective view of a compressor blade,as embodied by the invention;

FIG. 5 is a end view of a compressor blade as viewed looking radiallyoutwardly from the blade tip, as embodied by the invention;

FIG. 6 is a view similar to FIG. 2; and

FIG. 7 is a cross-sectional view thereof taken generally about on line7-7 in FIG. 6.

DETAILED DESCRIPTION OF THE INVENTION

In accordance with one embodiment of the instant invention, an articleof manufacture has a nominal profile substantially in accordance withCartesian coordinate values of X, Y and Z set forth in TABLE A, andwherein X and Y are distances in inches which, when connected by smoothcontinuing arcs, define airfoil profile sections at each distance Z ininches, the profile sections at the Z distances being joined smoothlywith one another to form a complete airfoil shape.

In accordance with one embodiment of the instant invention, there isprovided an airfoil compressor shape for a vane of a gas turbine thatenhances the performance of the gas turbine. The airfoil shape hereofalso improves the interaction between various stages of the compressorand affords improved aerodynamic efficiency, while simultaneouslyreducing stage airfoil thermal and mechanical stresses.

The vane airfoil profile, as embodied by the invention, is defined by aunique loci of points to achieve the necessary efficiency and loadingrequirements whereby improved compressor performance is obtained. Theseunique loci of points define the nominal airfoil profile and areidentified by the X, Y and Z Cartesian coordinates of the TABLE A thatfollows. The points for the coordinate values shown in TABLE A arerelative to the engine centerline and for a cold, i.e., room temperaturevane at various cross-sections of the vane's airfoil along its length.The positive X, Y and Z directions are axial toward the exhaust end ofthe turbine, tangential in the direction of engine rotation and radiallyoutwardly toward the static case, respectively. The X, Y, and Zcoordinates are given in distance dimensions, e.g., units of inches, andare joined smoothly at each Z location to form a smooth continuousairfoil cross-section. Each defined airfoil section in the X, Y plane isjoined smoothly with adjacent airfoil sections in the Z direction toform the complete airfoil shape.

It will be appreciated that an airfoil heats up during use, as known bya person of ordinary skill in the art. The airfoil profile will thuschange as a result of mechanical loading and temperature. Accordingly,the cold or room temperature profile, for manufacturing purposes, isgiven by X, Y and Z coordinates. A distance of plus or minus about 0.160inches (+/−0.160″) from the nominal profile in a direction normal to anysurface location along the nominal profile and which includes anycoating, defines a profile envelope for this vane airfoil, because amanufactured vane airfoil profile may be different from the nominalairfoil profile given by the following tables. The airfoil shape isrobust to this variation, without impairment of the mechanical andaerodynamic functions of the vane.

The airfoil, as embodied by the invention, can be scaled up or scaleddown geometrically for introduction into similar turbine designs.Consequently, the X, Y and Z coordinates of the nominal airfoil profilemay be a function of a constant. That is, the X, Y and Z coordinatevalues may be multiplied or divided by the same constant or number toprovide a “scaled-up” or “scaled-down” version of the vane airfoilprofile, while retaining the airfoil section shape, as embodied by theinvention.

Referring now to FIG. 1, there is illustrated a portion of a compressor,generally designated 10, having multiple stages including a first stage,generally designated 12. Each stage includes a plurality ofcircumferentially spaced stator blades, as well as rotor blades 14mounted on the compressor rotor 16. The first stage compressor statorblades 12 are circumferentially spaced one from the other, havingairfoils 18 of a particular airfoil shape or profile specified below.Referring to FIG. 2, the airfoil shape or profile includes leading andtrailing edges 20 and 22, respectively.

Referring now to FIGS. 2-7, each of the airfoils blades has an airfoilprofile defined by a Cartesian coordinate system for X, Y and Z values.The coordinate values are set forth in inches in Table I below. TheCartesian coordinate system includes orthogonally related X, Y and Zaxes with the Z axis extending along a radius from the centerline of thecompressor rotor, i.e., normal to a plane containing the X and Y values.The Z distance commences at zero in the X, Y plane at the radiallyoutermost aerodynamic section. This Z distance, i.e., Z=0, is located ona radius 17.114 inches from the compressor centerline. The X axis liesparallel to the compressor rotor centerline, i.e., the rotary axis. Bydefining X and Y coordinate values at selected locations in a Zdirection normal to the X, Y plane, the profile of airfoil 20 can beascertained. By connecting the X and Y values with smooth continuingarcs, each profile section at each distance Z is fixed. The surfaceprofiles at the various surface locations between the distances Z areconnected smoothly to one another to form the airfoil. The tabularvalues given in Table I below are in inches and represent airfoilprofiles at ambient, non-operating or non-hot conditions and are for anuncoated airfoil. The sign convention assigns a positive value Z in aradially inward direction and positive and negative values for the X andY coordinate values as typically used in Cartesian coordinate systems.

To define the airfoil shape of the vane airfoil, a unique set or loci ofpoints in space are provided. This unique set or loci of points meet thestage requirements so the stage can be manufactured. This unique loci ofpoints also meets the desired requirements for stage efficiency andreduced thermal and mechanical stresses. The loci of points are arrivedat by iteration between aerodynamic and mechanical loadings enabling thecompressor to run in an efficient, safe and smooth manner.

The loci, as embodied by the invention, defines the vane airfoil profileand can comprise a set of points relative to the axis of rotation of theengine. For example, a set of points can be provided to define a vaneairfoil profile. Furthermore, the vane airfoil profile, as embodied bythe invention, can comprise a vanes for a Stage 4 rotor vane of acompressor.

A Cartesian coordinate system of X, Y and Z values given in TABLE Abelow defines a profile of a vane airfoil at various locations along itslength. The coordinate values for the X, Y and Z coordinates are setforth in inches, although other units of dimensions may be used when thevalues are appropriately converted. These values exclude fillet regionsof the platform. The Cartesian coordinate system hasorthogonally-related X, Y and Z axes. The X axis lies parallel to thecompressor rotor centerline, such as the rotary axis. A positive Xcoordinate value is axial toward the aft, for example the exhaust end ofthe compressor. A positive Y coordinate value directed aft extendstangentially in the direction of rotation of the rotor. A positive Zcoordinate value is directed radially outward toward the static casingof the compressor.

TABLE A values are generated and shown to three decimal places fordetermining the profile of the airfoil. There are typical manufacturingtolerances as well as coatings, which should be accounted for in theactual profile of the airfoil. Accordingly, the values for the profilegiven are for a nominal airfoil. It will therefore be appreciated that+/− typical manufacturing tolerances, such as, +/− values, including anycoating thicknesses, are additive to the X and Y values. Therefore, adistance of about +/−0.160 inches in a direction normal to any surfacelocation along the airfoil profile defines an airfoil profile envelopefor a vane airfoil design and compressor. In other words, a distance ofabout +/−0.160 inches in a direction normal to any surface locationalong the airfoil profile defines a range of variation between measuredpoints on the actual airfoil surface at nominal cold or room temperatureand the ideal position of those points, at the same temperature, asembodied by the invention. The vane airfoil design, as embodied by theinvention, is robust to this range of variation without impairment ofmechanical and aerodynamic functions.

The coordinate values given in the TABLE A below provide the nominalprofile envelope for an exemplary S1 stage rotor.

TABLE A X Y Z −0.6271 1.1132 −0.2140 −0.6265 1.1134 −0.2140 −0.62541.1138 −0.2140 −0.6231 1.1143 −0.2140 −0.6185 1.1149 −0.2140 −0.61121.1144 −0.2140 −0.5986 1.1105 −0.2140 −0.5837 1.1013 −0.2140 −0.56681.0856 −0.2140 −0.5483 1.0635 −0.2140 −0.5253 1.0338 −0.2140 −0.49970.9990 −0.2140 −0.4730 0.9613 −0.2140 −0.4436 0.9185 −0.2140 −0.41140.8707 −0.2140 −0.3762 0.8179 −0.2140 −0.3399 0.7624 −0.2140 −0.30200.7044 −0.2140 −0.2624 0.6441 −0.2140 −0.2210 0.5816 −0.2140 −0.17770.5169 −0.2140 −0.1324 0.4500 −0.2140 −0.0852 0.3810 −0.2140 −0.03610.3097 −0.2140 0.0132 0.2386 −0.2140 0.0628 0.1677 −0.2140 0.1124 0.0968−0.2140 0.1620 0.0259 −0.2140 0.2114 −0.0452 −0.2140 0.2605 −0.1165−0.2140 0.3095 −0.1878 −0.2140 0.3585 −0.2591 −0.2140 0.4077 −0.3304−0.2140 0.4571 −0.4014 −0.2140 0.5069 −0.4722 −0.2140 0.5555 −0.5402−0.2140 0.6030 −0.6056 −0.2140 0.6492 −0.6683 −0.2140 0.6941 −0.7283−0.2140 0.7379 −0.7856 −0.2140 0.7804 −0.8403 −0.2140 0.8216 −0.8923−0.2140 0.8596 −0.9394 −0.2140 0.8944 −0.9818 −0.2140 0.9258 −1.0194−0.2140 0.9540 −1.0523 −0.2140 0.9788 −1.0804 −0.2140 1.0000 −1.1040−0.2140 1.0184 −1.1240 −0.2140 1.0338 −1.1408 −0.2140 1.0466 −1.1545−0.2140 1.0569 −1.1654 −0.2140 1.0637 −1.1747 −0.2140 1.0654 −1.1832−0.2140 1.0642 −1.1903 −0.2140 1.0616 −1.1955 −0.2140 1.0589 −1.1989−0.2140 1.0554 −1.2018 −0.2140 1.0501 −1.2044 −0.2140 1.0427 −1.2055−0.2140 1.0341 −1.2035 −0.2140 1.0246 −1.1962 −0.2140 1.0131 −1.1858−0.2140 0.9986 −1.1729 −0.2140 0.9810 −1.1572 −0.2140 0.9600 −1.1387−0.2140 0.9352 −1.1171 −0.2140 0.9056 −1.0920 −0.2140 0.8712 −1.0634−0.2140 0.8319 −1.0313 −0.2140 0.7878 −0.9956 −0.2140 0.7390 −0.9562−0.2140 0.6856 −0.9132 −0.2140 0.6299 −0.8682 −0.2140 0.5720 −0.8211−0.2140 0.5121 −0.7719 −0.2140 0.4504 −0.7202 −0.2140 0.3870 −0.6661−0.2140 0.3222 −0.6092 −0.2140 0.2560 −0.5496 −0.2140 0.1910 −0.4888−0.2140 0.1273 −0.4268 −0.2140 0.0651 −0.3633 −0.2140 0.0046 −0.2982−0.2140 −0.0539 −0.2313 −0.2140 −0.1104 −0.1623 −0.2140 −0.1646 −0.0912−0.2140 −0.2166 −0.0180 −0.2140 −0.2664 0.0573 −0.2140 −0.3140 0.1342−0.2140 −0.3592 0.2125 −0.2140 −0.4007 0.2894 −0.2140 −0.4386 0.3648−0.2140 −0.4731 0.4386 −0.2140 −0.5043 0.5105 −0.2140 −0.5319 0.5807−0.2140 −0.5567 0.6487 −0.2140 −0.5793 0.7143 −0.2140 −0.5981 0.7780−0.2140 −0.6139 0.8363 −0.2140 −0.6269 0.8891 −0.2140 −0.6368 0.9364−0.2140 −0.6446 0.9810 −0.2140 −0.6499 1.0199 −0.2140 −0.6526 1.0500−0.2140 −0.6516 1.0740 −0.2140 −0.6471 1.0916 −0.2140 −0.6403 1.1033−0.2140 −0.6350 1.1087 −0.2140 −0.6310 1.1114 −0.2140 −0.6288 1.1125−0.2140 −0.6276 1.1130 −0.2140 −0.6268 1.1302 0.0000 −0.6262 1.13040.0000 −0.6251 1.1308 0.0000 −0.6229 1.1314 0.0000 −0.6183 1.1322 0.0000−0.6110 1.1320 0.0000 −0.5984 1.1284 0.0000 −0.5835 1.1196 0.0000−0.5664 1.1042 0.0000 −0.5478 1.0823 0.0000 −0.5249 1.0526 0.0000−0.4992 1.0178 0.0000 −0.4726 0.9802 0.0000 −0.4434 0.9373 0.0000−0.4113 0.8895 0.0000 −0.3762 0.8366 0.0000 −0.3400 0.7811 0.0000−0.3022 0.7231 0.0000 −0.2628 0.6628 0.0000 −0.2216 0.6001 0.0000−0.1786 0.5353 0.0000 −0.1337 0.4682 0.0000 −0.0870 0.3989 0.0000−0.0384 0.3273 0.0000 0.0103 0.2559 0.0000 0.0591 0.1845 0.0000 0.10780.1131 0.0000 0.1564 0.0415 0.0000 0.2048 −0.0302 0.0000 0.2529 −0.10200.0000 0.3008 −0.1741 0.0000 0.3486 −0.2461 0.0000 0.3965 −0.3181 0.00000.4447 −0.3900 0.0000 0.4931 −0.4616 0.0000 0.5402 −0.5307 0.0000 0.5861−0.5970 0.0000 0.6307 −0.6608 0.0000 0.6741 −0.7219 0.0000 0.7162−0.7804 0.0000 0.7570 −0.8363 0.0000 0.7965 −0.8895 0.0000 0.8330−0.9379 0.0000 0.8662 −0.9814 0.0000 0.8962 −1.0201 0.0000 0.9231−1.0540 0.0000 0.9467 −1.0831 0.0000 0.9669 −1.1076 0.0000 0.9843−1.1283 0.0000 0.9991 −1.1457 0.0000 1.0112 −1.1600 0.0000 1.0210−1.1713 0.0000 1.0279 −1.1805 0.0000 1.0300 −1.1889 0.0000 1.0289−1.1962 0.0000 1.0262 −1.2014 0.0000 1.0233 −1.2048 0.0000 1.0198−1.2074 0.0000 1.0143 −1.2097 0.0000 1.0069 −1.2102 0.0000 0.9986−1.2073 0.0000 0.9897 −1.1994 0.0000 0.9788 −1.1886 0.0000 0.9650−1.1750 0.0000 0.9483 −1.1587 0.0000 0.9282 −1.1393 0.0000 0.9046−1.1167 0.0000 0.8764 −1.0905 0.0000 0.8435 −1.0605 0.0000 0.8059−1.0269 0.0000 0.7637 −0.9896 0.0000 0.7169 −0.9484 0.0000 0.6656−0.9035 0.0000 0.6121 −0.8565 0.0000 0.5564 −0.8076 0.0000 0.4988−0.7564 0.0000 0.4394 −0.7029 0.0000 0.3784 −0.6469 0.0000 0.3159−0.5882 0.0000 0.2522 −0.5268 0.0000 0.1896 −0.4643 0.0000 0.1282−0.4008 0.0000 0.0682 −0.3360 0.0000 0.0099 −0.2698 0.0000 −0.0466−0.2020 0.0000 −0.1011 −0.1324 0.0000 −0.1536 −0.0610 0.0000 −0.20420.0120 0.0000 −0.2530 0.0867 0.0000 −0.3000 0.1628 0.0000 −0.3453 0.24050.0000 −0.3871 0.3166 0.0000 −0.4256 0.3911 0.0000 −0.4609 0.4639 0.0000−0.4931 0.5348 0.0000 −0.5219 0.6040 0.0000 −0.5480 0.6710 0.0000−0.5717 0.7357 0.0000 −0.5918 0.7984 0.0000 −0.6088 0.8558 0.0000−0.6228 0.9078 0.0000 −0.6336 0.9545 0.0000 −0.6421 0.9986 0.0000−0.6481 1.0371 0.0000 −0.6512 1.0669 0.0000 −0.6504 1.0907 0.0000−0.6460 1.1081 0.0000 −0.6396 1.1200 0.0000 −0.6344 1.1255 0.0000−0.6305 1.1283 0.0000 −0.6284 1.1294 0.0000 −0.6273 1.1299 0.0000−0.6270 1.1355 0.0600 −0.6265 1.1357 0.0600 −0.6254 1.1361 0.0600−0.6231 1.1367 0.0600 −0.6185 1.1375 0.0600 −0.6113 1.1373 0.0600−0.5987 1.1338 0.0600 −0.5837 1.1250 0.0600 −0.5666 1.1097 0.0600−0.5479 1.0878 0.0600 −0.5249 1.0582 0.0600 −0.4992 1.0234 0.0600−0.4726 0.9858 0.0600 −0.4434 0.9429 0.0600 −0.4113 0.8950 0.0600−0.3763 0.8421 0.0600 −0.3401 0.7866 0.0600 −0.3024 0.7285 0.0600−0.2630 0.6682 0.0600 −0.2219 0.6055 0.0600 −0.1789 0.5406 0.0600−0.1341 0.4734 0.0600 −0.0876 0.4040 0.0600 −0.0392 0.3323 0.0600 0.00930.2607 0.0600 0.0579 0.1891 0.0600 0.1065 0.1175 0.0600 0.1548 0.04580.0600 0.2029 −0.0261 0.0600 0.2507 −0.0982 0.0600 0.2982 −0.1704 0.06000.3458 −0.2427 0.0600 0.3934 −0.3149 0.0600 0.4411 −0.3870 0.0600 0.4892−0.4589 0.0600 0.5359 −0.5282 0.0600 0.5814 −0.5949 0.0600 0.6257−0.6590 0.0600 0.6686 −0.7204 0.0600 0.7103 −0.7792 0.0600 0.7506−0.8354 0.0600 0.7897 −0.8890 0.0600 0.8257 −0.9377 0.0600 0.8585−0.9815 0.0600 0.8882 −1.0205 0.0600 0.9147 −1.0547 0.0600 0.9380−1.0841 0.0600 0.9579 −1.1088 0.0600 0.9751 −1.1297 0.0600 0.9896−1.1473 0.0600 1.0016 −1.1617 0.0600 1.0112 −1.1732 0.0600 1.0181−1.1824 0.0600 1.0201 −1.1909 0.0600 1.0189 −1.1981 0.0600 1.0162−1.2033 0.0600 1.0133 −1.2066 0.0600 1.0097 −1.2092 0.0600 1.0042−1.2114 0.0600 0.9968 −1.2118 0.0600 0.9885 −1.2088 0.0600 0.9798−1.2008 0.0600 0.9690 −1.1898 0.0600 0.9555 −1.1761 0.0600 0.9389−1.1595 0.0600 0.9192 −1.1399 0.0600 0.8959 −1.1171 0.0600 0.8681−1.0904 0.0600 0.8357 −1.0600 0.0600 0.7986 −1.0260 0.0600 0.7569−0.9881 0.0600 0.7108 −0.9464 0.0600 0.6601 −0.9008 0.0600 0.6073−0.8533 0.0600 0.5523 −0.8037 0.0600 0.4953 −0.7519 0.0600 0.4366−0.6978 0.0600 0.3762 −0.6413 0.0600 0.3144 −0.5821 0.0600 0.2514−0.5202 0.0600 0.1894 −0.4574 0.0600 0.1287 −0.3935 0.0600 0.0694−0.3285 0.0600 0.0117 −0.2622 0.0600 −0.0443 −0.1944 0.0600 −0.0982−0.1250 0.0600 −0.1502 −0.0540 0.0600 −0.2003 0.0186 0.0600 −0.24860.0927 0.0600 −0.2952 0.1682 0.0600 −0.3400 0.2451 0.0600 −0.3817 0.32080.0600 −0.4203 0.3953 0.0600 −0.4559 0.4681 0.0600 −0.4884 0.5390 0.0600−0.5176 0.6082 0.0600 −0.5441 0.6752 0.0600 −0.5683 0.7399 0.0600−0.5889 0.8027 0.0600 −0.6064 0.8602 0.0600 −0.6209 0.9123 0.0600−0.6321 0.9591 0.0600 −0.6412 1.0033 0.0600 −0.6475 1.0418 0.0600−0.6508 1.0717 0.0600 −0.6503 1.0956 0.0600 −0.6461 1.1131 0.0600−0.6398 1.1251 0.0600 −0.6347 1.1307 0.0600 −0.6308 1.1335 0.0600−0.6287 1.1347 0.0600 −0.6276 1.1352 0.0600 −0.6268 1.1452 0.1710−0.6263 1.1455 0.1710 −0.6252 1.1459 0.1710 −0.6230 1.1465 0.1710−0.6184 1.1473 0.1710 −0.6111 1.1471 0.1710 −0.5985 1.1436 0.1710−0.5835 1.1349 0.1710 −0.5663 1.1197 0.1710 −0.5474 1.0980 0.1710−0.5244 1.0684 0.1710 −0.4987 1.0336 0.1710 −0.4721 0.9959 0.1710−0.4429 0.9530 0.1710 −0.4108 0.9051 0.1710 −0.3759 0.8521 0.1710−0.3398 0.7965 0.1710 −0.3022 0.7384 0.1710 −0.2629 0.6779 0.1710−0.2220 0.6151 0.1710 −0.1792 0.5500 0.1710 −0.1347 0.4827 0.1710−0.0884 0.4130 0.1710 −0.0405 0.3410 0.1710 0.0077 0.2691 0.1710 0.05590.1973 0.1710 0.1039 0.1253 0.1710 0.1517 0.0532 0.1710 0.1992 −0.01910.1710 0.2463 −0.0917 0.1710 0.2932 −0.1644 0.1710 0.3400 −0.2371 0.17100.3869 −0.3098 0.1710 0.4340 −0.3824 0.1710 0.4812 −0.4549 0.1710 0.5272−0.5248 0.1710 0.5718 −0.5920 0.1710 0.6152 −0.6567 0.1710 0.6573−0.7188 0.1710 0.6980 −0.7782 0.1710 0.7375 −0.8351 0.1710 0.7756−0.8894 0.1710 0.8107 −0.9387 0.1710 0.8426 −0.9833 0.1710 0.8715−1.0229 0.1710 0.8972 −1.0576 0.1710 0.9199 −1.0876 0.1710 0.9392−1.1127 0.1710 0.9559 −1.1341 0.1710 0.9700 −1.1520 0.1710 0.9816−1.1667 0.1710 0.9909 −1.1785 0.1710 0.9975 −1.1879 0.1710 0.9992−1.1963 0.1710 0.9978 −1.2034 0.1710 0.9950 −1.2084 0.1710 0.9920−1.2116 0.1710 0.9884 −1.2141 0.1710 0.9828 −1.2162 0.1710 0.9755−1.2164 0.1710 0.9673 −1.2132 0.1710 0.9589 −1.2049 0.1710 0.9484−1.1936 0.1710 0.9353 −1.1796 0.1710 0.9194 −1.1626 0.1710 0.9002−1.1425 0.1710 0.8777 −1.1192 0.1710 0.8507 −1.0919 0.1710 0.8193−1.0608 0.1710 0.7833 −1.0258 0.1710 0.7429 −0.9870 0.1710 0.6980−0.9443 0.1710 0.6488 −0.8976 0.1710 0.5974 −0.8490 0.1710 0.5438−0.7982 0.1710 0.4883 −0.7454 0.1710 0.4310 −0.6902 0.1710 0.3720−0.6326 0.1710 0.3115 −0.5724 0.1710 0.2498 −0.5095 0.1710 0.1890−0.4457 0.1710 0.1294 −0.3810 0.1710 0.0711 −0.3153 0.1710 0.0142−0.2483 0.1710 −0.0411 −0.1799 0.1710 −0.0945 −0.1100 0.1710 −0.1460−0.0386 0.1710 −0.1957 0.0344 0.1710 −0.2437 0.1088 0.1710 −0.29000.1845 0.1710 −0.3348 0.2616 0.1710 −0.3764 0.3375 0.1710 −0.4148 0.41160.1710 −0.4502 0.4839 0.1710 −0.4827 0.5543 0.1710 −0.5121 0.6229 0.1710−0.5389 0.6893 0.1710 −0.5635 0.7533 0.1710 −0.5847 0.8154 0.1710−0.6027 0.8723 0.1710 −0.6178 0.9238 0.1710 −0.6296 0.9701 0.1710−0.6392 1.0138 0.1710 −0.6461 1.0520 0.1710 −0.6498 1.0816 0.1710−0.6494 1.1052 0.1710 −0.6455 1.1226 0.1710 −0.6394 1.1347 0.1710−0.6344 1.1403 0.1710 −0.6306 1.1432 0.1710 −0.6285 1.1445 0.1710−0.6274 1.1450 0.1710 −0.6255 1.1512 0.2400 −0.6250 1.1514 0.2400−0.6239 1.1518 0.2400 −0.6216 1.1525 0.2400 −0.6171 1.1533 0.2400−0.6098 1.1531 0.2400 −0.5972 1.1495 0.2400 −0.5822 1.1409 0.2400−0.5649 1.1257 0.2400 −0.5460 1.1040 0.2400 −0.5230 1.0744 0.2400−0.4974 1.0396 0.2400 −0.4708 1.0019 0.2400 −0.4416 0.9590 0.2400−0.4097 0.9110 0.2400 −0.3748 0.8580 0.2400 −0.3388 0.8023 0.2400−0.3013 0.7441 0.2400 −0.2622 0.6836 0.2400 −0.2214 0.6207 0.2400−0.1788 0.5555 0.2400 −0.1346 0.4880 0.2400 −0.0886 0.4181 0.2400−0.0410 0.3459 0.2400 0.0068 0.2738 0.2400 0.0545 0.2017 0.2400 0.10220.1295 0.2400 0.1495 0.0571 0.2400 0.1965 −0.0155 0.2400 0.2431 −0.08840.2400 0.2894 −0.1614 0.2400 0.3357 −0.2345 0.2400 0.3821 −0.3075 0.24000.4285 −0.3805 0.2400 0.4751 −0.4534 0.2400 0.5203 −0.5236 0.2400 0.5643−0.5913 0.2400 0.6070 −0.6564 0.2400 0.6483 −0.7189 0.2400 0.6884−0.7789 0.2400 0.7271 −0.8362 0.2400 0.7645 −0.8910 0.2400 0.7988−0.9409 0.2400 0.8300 −0.9859 0.2400 0.8582 −1.0260 0.2400 0.8834−1.0612 0.2400 0.9055 −1.0914 0.2400 0.9244 −1.1169 0.2400 0.9407−1.1386 0.2400 0.9544 −1.1567 0.2400 0.9657 −1.1717 0.2400 0.9748−1.1836 0.2400 0.9812 −1.1931 0.2400 0.9828 −1.2016 0.2400 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0.2400−0.6148 0.9308 0.2400 −0.6270 0.9768 0.2400 −0.6369 1.0202 0.2400−0.6441 1.0582 0.2400 −0.6479 1.0876 0.2400 −0.6476 1.1112 0.2400−0.6438 1.1287 0.2400 −0.6379 1.1406 0.2400 −0.6330 1.1463 0.2400−0.6292 1.1492 0.2400 −0.6271 1.1504 0.2400 −0.6261 1.1509 0.2400−0.6231 1.1563 0.3000 −0.6226 1.1565 0.3000 −0.6215 1.1569 0.3000−0.6193 1.1576 0.3000 −0.6147 1.1584 0.3000 −0.6074 1.1582 0.3000−0.5949 1.1545 0.3000 −0.5799 1.1458 0.3000 −0.5626 1.1307 0.3000−0.5437 1.1090 0.3000 −0.5208 1.0793 0.3000 −0.4952 1.0445 0.3000−0.4688 1.0068 0.3000 −0.4397 0.9639 0.3000 −0.4078 0.9159 0.3000−0.3730 0.8628 0.3000 −0.3372 0.8071 0.3000 −0.2998 0.7489 0.3000−0.2609 0.6883 0.3000 −0.2203 0.6253 0.3000 −0.1781 0.5600 0.3000−0.1341 0.4923 0.3000 −0.0885 0.4223 0.3000 −0.0413 0.3499 0.3000 0.00600.2775 0.3000 0.0533 0.2052 0.3000 0.1004 0.1327 0.3000 0.1472 0.06010.3000 0.1936 −0.0129 0.3000 0.2397 −0.0860 0.3000 0.2854 −0.1593 0.30000.3311 −0.2327 0.3000 0.3768 −0.3061 0.3000 0.4225 −0.3794 0.3000 0.4684−0.4527 0.3000 0.5129 −0.5234 0.3000 0.5561 −0.5915 0.3000 0.5981−0.6571 0.3000 0.6386 −0.7200 0.3000 0.6778 −0.7804 0.3000 0.7158−0.8383 0.3000 0.7523 −0.8935 0.3000 0.7859 −0.9439 0.3000 0.8164−0.9893 0.3000 0.8439 −1.0299 0.3000 0.8685 −1.0654 0.3000 0.8900−1.0961 0.3000 0.9085 −1.1218 0.3000 0.9244 −1.1438 0.3000 0.9378−1.1622 0.3000 0.9488 −1.1773 0.3000 0.9577 −1.1893 0.3000 0.9641−1.1989 0.3000 0.9657 −1.2075 0.3000 0.9641 −1.2147 0.3000 0.9612−1.2197 0.3000 0.9581 −1.2229 0.3000 0.9544 −1.2253 0.3000 0.9488−1.2271 0.3000 0.9415 −1.2270 0.3000 0.9335 −1.2235 0.3000 0.9255−1.2149 0.3000 0.9155 −1.2033 0.3000 0.9030 −1.1889 0.3000 0.8878−1.1714 0.3000 0.8695 −1.1507 0.3000 0.8480 −1.1266 0.3000 0.8223−1.0984 0.3000 0.7922 −1.0663 0.3000 0.7578 −1.0302 0.3000 0.7190−0.9901 0.3000 0.6760 −0.9460 0.3000 0.6288 −0.8978 0.3000 0.5793−0.8476 0.3000 0.5278 −0.7954 0.3000 0.4744 −0.7410 0.3000 0.4191−0.6843 0.3000 0.3621 −0.6251 0.3000 0.3037 −0.5635 0.3000 0.2439−0.4991 0.3000 0.1849 −0.4340 0.3000 0.1270 −0.3680 0.3000 0.0702−0.3011 0.3000 0.0147 −0.2331 0.3000 −0.0393 −0.1639 0.3000 −0.0916−0.0933 0.3000 −0.1423 −0.0212 0.3000 −0.1912 0.0523 0.3000 −0.23850.1272 0.3000 −0.2843 0.2033 0.3000 −0.3284 0.2803 0.3000 −0.3693 0.35560.3000 −0.4072 0.4293 0.3000 −0.4423 0.5011 0.3000 −0.4745 0.5709 0.3000−0.5040 0.6388 0.3000 −0.5309 0.7046 0.3000 −0.5557 0.7680 0.3000−0.5773 0.8294 0.3000 −0.5958 0.8857 0.3000 −0.6113 0.9367 0.3000−0.6236 0.9824 0.3000 −0.6338 1.0256 0.3000 −0.6412 1.0634 0.3000−0.6451 1.0927 0.3000 −0.6449 1.1163 0.3000 −0.6412 1.1337 0.3000−0.6354 1.1457 0.3000 −0.6306 1.1513 0.3000 −0.6268 1.1543 0.3000−0.6248 1.1555 0.3000 −0.6237 1.1560 0.3000 −0.6147 1.1658 0.4280−0.6141 1.1660 0.4280 −0.6131 1.1664 0.4280 −0.6108 1.1671 0.4280−0.6063 1.1679 0.4280 −0.5990 1.1676 0.4280 −0.5866 1.1638 0.4280−0.5716 1.1550 0.4280 −0.5544 1.1398 0.4280 −0.5355 1.1180 0.4280−0.5128 1.0883 0.4280 −0.4875 1.0533 0.4280 −0.4613 1.0155 0.4280−0.4325 0.9724 0.4280 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1.1431 0.4280 −0.6267 1.1551 0.4280−0.6220 1.1608 0.4280 −0.6183 1.1638 0.4280 −0.6163 1.1650 0.4280−0.6152 1.1655 0.4280 −0.6037 1.1710 0.5570 −0.6032 1.1713 0.5570−0.6021 1.1717 0.5570 −0.5999 1.1724 0.5570 −0.5953 1.1731 0.5570−0.5881 1.1727 0.5570 −0.5757 1.1688 0.5570 −0.5608 1.1598 0.5570−0.5437 1.1446 0.5570 −0.5248 1.1228 0.5570 −0.5025 1.0928 0.5570−0.4776 1.0577 0.5570 −0.4517 1.0197 0.5570 −0.4233 0.9764 0.5570−0.3922 0.9281 0.5570 −0.3584 0.8747 0.5570 −0.3235 0.8185 0.5570−0.2874 0.7598 0.5570 −0.2498 0.6986 0.5570 −0.2108 0.6349 0.5570−0.1703 0.5687 0.5570 −0.1283 0.5001 0.5570 −0.0849 0.4289 0.5570−0.0402 0.3553 0.5570 0.0046 0.2816 0.5570 0.0492 0.2078 0.5570 0.09350.1339 0.5570 0.1375 0.0598 0.5570 0.1811 −0.0146 0.5570 0.2242 −0.08920.5570 0.2669 −0.1641 0.5570 0.3094 −0.2391 0.5570 0.3517 −0.3142 0.55700.3939 −0.3894 0.5570 0.4360 −0.4646 0.5570 0.4768 −0.5373 0.5570 0.5164−0.6074 0.5570 0.5546 −0.6749 0.5570 0.5915 −0.7399 0.5570 0.6271−0.8023 0.5570 0.6614 −0.8621 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0.6938−1.1576 0.8140 0.6682 −1.1226 0.8140 0.6390 −1.0831 0.8140 0.6061−1.0392 0.8140 0.5696 −0.9908 0.8140 0.5295 −0.9378 0.8140 0.4876−0.8826 0.8140 0.4439 −0.8251 0.8140 0.3986 −0.7653 0.8140 0.3517−0.7030 0.8140 0.3033 −0.6383 0.8140 0.2535 −0.5711 0.8140 0.2025−0.5013 0.8140 0.1521 −0.4311 0.8140 0.1025 −0.3604 0.8140 0.0537−0.2892 0.8140 0.0060 −0.2174 0.8140 −0.0407 −0.1449 0.8140 −0.0860−0.0717 0.8140 −0.1299 0.0024 0.8140 −0.1726 0.0773 0.8140 −0.21410.1528 0.8140 −0.2545 0.2291 0.8140 −0.2939 0.3059 0.8140 −0.3308 0.38090.8140 −0.3655 0.4539 0.8140 −0.3978 0.5249 0.8140 −0.4280 0.5939 0.8140−0.4560 0.6608 0.8140 −0.4819 0.7256 0.8140 −0.5058 0.7881 0.8140−0.5274 0.8483 0.8140 −0.5461 0.9034 0.8140 −0.5619 0.9533 0.8140−0.5750 0.9980 0.8140 −0.5862 1.0402 0.8140 −0.5945 1.0771 0.8140−0.5983 1.1059 0.8140 −0.5983 1.1290 0.8140 −0.5953 1.1462 0.8140−0.5902 1.1583 0.8140 −0.5858 1.1641 0.8140 −0.5822 1.1671 0.8140−0.5802 1.1683 0.8140 −0.5792 1.1689 0.8140 −0.5355 1.1218 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1.3280 0.6867−1.2440 1.3280 0.6990 −1.2672 1.3280 0.7095 −1.2866 1.3280 0.7182−1.3025 1.3280 0.7252 −1.3153 1.3280 0.7302 −1.3252 1.3280 0.7307−1.3336 1.3280 0.7284 −1.3402 1.3280 0.7250 −1.3446 1.3280 0.7216−1.3472 1.3280 0.7177 −1.3489 1.3280 0.7121 −1.3499 1.3280 0.7052−1.3486 1.3280 0.6982 −1.3438 1.3280 0.6919 −1.3344 1.3280 0.6841−1.3220 1.3280 0.6743 −1.3064 1.3280 0.6624 −1.2876 1.3280 0.6482−1.2652 1.3280 0.6314 −1.2390 1.3280 0.6113 −1.2083 1.3280 0.5879−1.1730 1.3280 0.5612 −1.1331 1.3280 0.5312 −1.0886 1.3280 0.4980−1.0395 1.3280 0.4616 −0.9857 1.3280 0.4237 −0.9296 1.3280 0.3842−0.8710 1.3280 0.3434 −0.8100 1.3280 0.3012 −0.7466 1.3280 0.2577−0.6806 1.3280 0.2132 −0.6121 1.3280 0.1676 −0.5409 1.3280 0.1227−0.4693 1.3280 0.0786 −0.3973 1.3280 0.0354 −0.3249 1.3280 −0.0069−0.2520 1.3280 −0.0482 −0.1786 1.3280 −0.0882 −0.1045 1.3280 −0.1271−0.0298 1.3280 −0.1650 0.0454 1.3280 −0.2020 0.1211 1.3280 −0.23810.1973 1.3280 −0.2734 0.2739 1.3280 −0.3066 0.3484 1.3280 −0.3379 0.42071.3280 −0.3673 0.4909 1.3280 −0.3948 0.5589 1.3280 −0.4204 0.6247 1.3280−0.4443 0.6882 1.3280 −0.4663 0.7496 1.3280 −0.4867 0.8085 1.3280−0.5044 0.8624 1.3280 −0.5197 0.9111 1.3280 −0.5325 0.9546 1.3280−0.5436 0.9957 1.3280 −0.5511 1.0318 1.3280 −0.5543 1.0600 1.3280−0.5541 1.0826 1.3280 −0.5513 1.0994 1.3280 −0.5466 1.1112 1.3280−0.5425 1.1170 1.3280 −0.5390 1.1199 1.3280 −0.5371 1.1211 1.3280−0.5360 1.1216 1.3280 −0.5216 1.0898 1.5910 −0.5211 1.0900 1.5910−0.5200 1.0903 1.5910 −0.5178 1.0908 1.5910 −0.5133 1.0908 1.5910−0.5065 1.0892 1.5910 −0.4955 1.0832 1.5910 −0.4827 1.0725 1.5910−0.4679 1.0560 1.5910 −0.4517 1.0335 1.5910 −0.4332 1.0028 1.5910−0.4139 0.9662 1.5910 −0.3942 0.9267 1.5910 −0.3724 0.8821 1.5910−0.3484 0.8325 1.5910 −0.3221 0.7777 1.5910 −0.2948 0.7205 1.5910−0.2664 0.6606 1.5910 −0.2368 0.5983 1.5910 −0.2059 0.5336 1.5910−0.1737 0.4664 1.5910 −0.1402 0.3968 1.5910 −0.1053 0.3248 1.5910−0.0691 0.2503 1.5910 −0.0328 0.1760 1.5910 0.0036 0.1016 1.5910 0.04010.0273 1.5910 0.0765 −0.0470 1.5910 0.1126 −0.1215 1.5910 0.1484 −0.19611.5910 0.1839 −0.2709 1.5910 0.2191 −0.3458 1.5910 0.2542 −0.4208 1.59100.2892 −0.4958 1.5910 0.3241 −0.5708 1.5910 0.3579 −0.6434 1.5910 0.3906−0.7134 1.5910 0.4222 −0.7808 1.5910 0.4528 −0.8457 1.5910 0.4824−0.9080 1.5910 0.5109 −0.9678 1.5910 0.5385 −1.0249 1.5910 0.5638−1.0770 1.5910 0.5869 −1.1241 1.5910 0.6077 −1.1662 1.5910 0.6262−1.2032 1.5910 0.6425 −1.2351 1.5910 0.6565 −1.2620 1.5910 0.6687−1.2850 1.5910 0.6789 −1.3042 1.5910 0.6874 −1.3200 1.5910 0.6943−1.3326 1.5910 0.6991 −1.3425 1.5910 0.6996 −1.3507 1.5910 0.6973−1.3573 1.5910 0.6939 −1.3616 1.5910 0.6905 −1.3641 1.5910 0.6867−1.3658 1.5910 0.6811 −1.3667 1.5910 0.6743 −1.3654 1.5910 0.6674−1.3606 1.5910 0.6613 −1.3513 1.5910 0.6537 −1.3389 1.5910 0.6441−1.3235 1.5910 0.6325 −1.3047 1.5910 0.6187 −1.2825 1.5910 0.6023−1.2565 1.5910 0.5827 −1.2260 1.5910 0.5599 −1.1909 1.5910 0.5339−1.1512 1.5910 0.5048 −1.1069 1.5910 0.4726 −1.0580 1.5910 0.4373−1.0044 1.5910 0.4005 −0.9484 1.5910 0.3623 −0.8900 1.5910 0.3228−0.8292 1.5910 0.2821 −0.7659 1.5910 0.2402 −0.7000 1.5910 0.1973−0.6315 1.5910 0.1535 −0.5604 1.5910 0.1105 −0.4890 1.5910 0.0682−0.4172 1.5910 0.0268 −0.3449 1.5910 −0.0136 −0.2721 1.5910 −0.0530−0.1989 1.5910 −0.0912 −0.1250 1.5910 −0.1284 −0.0507 1.5910 −0.16460.0241 1.5910 −0.2000 0.0994 1.5910 −0.2346 0.1750 1.5910 −0.2684 0.25101.5910 −0.3003 0.3248 1.5910 −0.3304 0.3965 1.5910 −0.3586 0.4660 1.5910−0.3850 0.5332 1.5910 −0.4098 0.5983 1.5910 −0.4328 0.6610 1.5910−0.4541 0.7216 1.5910 −0.4738 0.7798 1.5910 −0.4912 0.8330 1.5910−0.5061 0.8812 1.5910 −0.5187 0.9242 1.5910 −0.5294 0.9648 1.5910−0.5365 1.0006 1.5910 −0.5394 1.0284 1.5910 −0.5393 1.0508 1.5910−0.5368 1.0674 1.5910 −0.5325 1.0792 1.5910 −0.5285 1.0850 1.5910−0.5251 1.0880 1.5910 −0.5232 1.0891 1.5910 −0.5222 1.0896 1.5910−0.5132 1.0584 1.8420 −0.5126 1.0585 1.8420 −0.5116 1.0588 1.8420−0.5094 1.0592 1.8420 −0.5049 1.0591 1.8420 −0.4983 1.0572 1.8420−0.4876 1.0509 1.8420 −0.4753 1.0400 1.8420 −0.4610 1.0233 1.8420−0.4454 1.0008 1.8420 −0.4275 0.9703 1.8420 −0.4089 0.9339 1.8420−0.3901 0.8945 1.8420 −0.3693 0.8501 1.8420 −0.3464 0.8006 1.8420−0.3213 0.7461 1.8420 −0.2950 0.6890 1.8420 −0.2677 0.6295 1.8420−0.2392 0.5676 1.8420 −0.2094 0.5032 1.8420 −0.1784 0.4365 1.8420−0.1460 0.3673 1.8420 −0.1122 0.2957 1.8420 −0.0771 0.2218 1.8420−0.0419 0.1480 1.8420 −0.0065 0.0742 1.8420 0.0291 0.0005 1.8420 0.0646−0.0733 1.8420 0.0999 −0.1471 1.8420 0.1350 −0.2210 1.8420 0.1697−0.2951 1.8420 0.2042 −0.3693 1.8420 0.2386 −0.4436 1.8420 0.2728−0.5179 1.8420 0.3070 −0.5923 1.8420 0.3402 −0.6641 1.8420 0.3722−0.7334 1.8420 0.4033 −0.8002 1.8420 0.4333 −0.8645 1.8420 0.4623−0.9262 1.8420 0.4904 −0.9854 1.8420 0.5174 −1.0420 1.8420 0.5423−1.0936 1.8420 0.5650 −1.1402 1.8420 0.5854 −1.1818 1.8420 0.6037−1.2184 1.8420 0.6197 −1.2501 1.8420 0.6335 −1.2767 1.8420 0.6454−1.2994 1.8420 0.6555 −1.3185 1.8420 0.6639 −1.3341 1.8420 0.6706−1.3466 1.8420 0.6754 −1.3564 1.8420 0.6758 −1.3645 1.8420 0.6735−1.3709 1.8420 0.6701 −1.3752 1.8420 0.6667 −1.3776 1.8420 0.6629−1.3793 1.8420 0.6574 −1.3801 1.8420 0.6507 −1.3788 1.8420 0.6439−1.3741 1.8420 0.6379 −1.3648 1.8420 0.6304 −1.3525 1.8420 0.6211−1.3372 1.8420 0.6097 −1.3186 1.8420 0.5961 −1.2966 1.8420 0.5800−1.2708 1.8420 0.5608 −1.2405 1.8420 0.5385 −1.2057 1.8420 0.5130−1.1663 1.8420 0.4845 −1.1223 1.8420 0.4530 −1.0737 1.8420 0.4185−1.0205 1.8420 0.3825 −0.9648 1.8420 0.3453 −0.9068 1.8420 0.3067−0.8463 1.8420 0.2670 −0.7833 1.8420 0.2263 −0.7178 1.8420 0.1846−0.6497 1.8420 0.1421 −0.5789 1.8420 0.1003 −0.5078 1.8420 0.0593−0.4363 1.8420 0.0192 −0.3644 1.8420 −0.0199 −0.2920 1.8420 −0.0579−0.2191 1.8420 −0.0948 −0.1457 1.8420 −0.1307 −0.0718 1.8420 −0.16570.0026 1.8420 −0.2000 0.0773 1.8420 −0.2335 0.1523 1.8420 −0.2663 0.22771.8420 −0.2973 0.3009 1.8420 −0.3265 0.3720 1.8420 −0.3539 0.4408 1.8420−0.3796 0.5075 1.8420 −0.4037 0.5719 1.8420 −0.4262 0.6340 1.8420−0.4469 0.6939 1.8420 −0.4662 0.7515 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−1.1669 3.4570 0.4910 −1.2076 3.4570 0.5085−1.2434 3.4570 0.5240 −1.2743 3.4570 0.5373 −1.3004 3.4570 0.5489−1.3225 3.4570 0.5588 −1.3411 3.4570 0.5670 −1.3563 3.4570 0.5736−1.3684 3.4570 0.5787 −1.3778 3.4570 0.5797 −1.3857 3.4570 0.5778−1.3921 3.4570 0.5745 −1.3964 3.4570 0.5712 −1.3989 3.4570 0.5675−1.4005 3.4570 0.5622 −1.4012 3.4570 0.5557 −1.3997 3.4570 0.5493−1.3947 3.4570 0.5436 −1.3857 3.4570 0.5362 −1.3738 3.4570 0.5270−1.3590 3.4570 0.5157 −1.3410 3.4570 0.5022 −1.3197 3.4570 0.4864−1.2948 3.4570 0.4674 −1.2654 3.4570 0.4455 −1.2316 3.4570 0.4206−1.1934 3.4570 0.3928 −1.1505 3.4570 0.3623 −1.1031 3.4570 0.3290−1.0511 3.4570 0.2945 −0.9967 3.4570 0.2589 −0.9398 3.4570 0.2223−0.8805 3.4570 0.1848 −0.8185 3.4570 0.1464 −0.7540 3.4570 0.1074−0.6868 3.4570 0.0680 −0.6169 3.4570 0.0295 −0.5463 3.4570 −0.0078−0.4752 3.4570 −0.0438 −0.4034 3.4570 −0.0786 −0.3310 3.4570 −0.1124−0.2580 3.4570 −0.1452 −0.1845 3.4570 −0.1774 −0.1106 3.4570 −0.2087−0.0363 3.4570 −0.2394 0.0383 3.4570 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−0.1330 0.1823 3.5120−0.1012 0.1090 3.5120 −0.0693 0.0358 3.5120 −0.0370 −0.0373 3.5120−0.0045 −0.1102 3.5120 0.0282 −0.1831 3.5120 0.0611 −0.2559 3.51200.0939 −0.3287 3.5120 0.1264 −0.4017 3.5120 0.1587 −0.4747 3.5120 0.1908−0.5479 3.5120 0.2228 −0.6211 3.5120 0.2538 −0.6918 3.5120 0.2838−0.7601 3.5120 0.3128 −0.8258 3.5120 0.3409 −0.8891 3.5120 0.3682−0.9498 3.5120 0.3946 −1.0080 3.5120 0.4202 −1.0636 3.5120 0.4439−1.1143 3.5120 0.4656 −1.1600 3.5120 0.4852 −1.2008 3.5120 0.5028−1.2367 3.5120 0.5182 −1.2677 3.5120 0.5316 −1.2938 3.5120 0.5432−1.3160 3.5120 0.5531 −1.3345 3.5120 0.5614 −1.3497 3.5120 0.5680−1.3619 3.5120 0.5730 −1.3713 3.5120 0.5738 −1.3791 3.5120 0.5718−1.3853 3.5120 0.5686 −1.3894 3.5120 0.5654 −1.3918 3.5120 0.5617−1.3934 3.5120 0.5563 −1.3941 3.5120 0.5498 −1.3926 3.5120 0.5435−1.3876 3.5120 0.5377 −1.3785 3.5120 0.5303 −1.3667 3.5120 0.5210−1.3518 3.5120 0.5097 −1.3339 3.5120 0.4961 −1.3125 3.5120 0.4802−1.2876 3.5120 0.4612 −1.2582 3.5120 0.4391 −1.2244 3.5120 0.4141−1.1861 3.5120 0.3862 −1.1432 3.5120 0.3556 −1.0958 3.5120 0.3222−1.0437 3.5120 0.2876 −0.9892 3.5120 0.2519 −0.9322 3.5120 0.2153−0.8727 3.5120 0.1778 −0.8106 3.5120 0.1395 −0.7459 3.5120 0.1006−0.6785 3.5120 0.0614 −0.6083 3.5120 0.0232 −0.5375 3.5120 −0.0137−0.4661 3.5120 −0.0493 −0.3939 3.5120 −0.0837 −0.3211 3.5120 −0.1169−0.2477 3.5120 −0.1493 −0.1739 3.5120 −0.1809 −0.0997 3.5120 −0.2118−0.0250 3.5120 −0.2419 0.0499 3.5120 −0.2712 0.1252 3.5120 −0.29970.2008 3.5120 −0.3264 0.2742 3.5120 −0.3515 0.3454 3.5120 −0.3749 0.41423.5120 −0.3967 0.4808 3.5120 −0.4170 0.5450 3.5120 −0.4358 0.6068 3.5120−0.4532 0.6663 3.5120 −0.4691 0.7234 3.5120 −0.4830 0.7754 3.5120−0.4949 0.8224 3.5120 −0.5049 0.8644 3.5120 −0.5137 0.9038 3.5120−0.5203 0.9382 3.5120 −0.5240 0.9649 3.5120 −0.5252 0.9864 3.5120−0.5245 1.0025 3.5120 −0.5222 1.0144 3.5120 −0.5195 1.0206 3.5120−0.5168 1.0239 3.5120 −0.5150 1.0251 3.5120 −0.5141 1.0256 3.5120−0.4995 1.0688 3.6410 −0.4990 1.0690 3.6410 −0.4979 1.0691 3.6410−0.4957 1.0690 3.6410 −0.4916 1.0676 3.6410 −0.4861 1.0636 3.6410−0.4779 1.0548 3.6410 −0.4688 1.0414 3.6410 −0.4584 1.0227 3.6410−0.4471 0.9985 3.6410 −0.4338 0.9664 3.6410 −0.4189 0.9292 3.6410−0.4033 0.8893 3.6410 −0.3860 0.8444 3.6410 −0.3668 0.7944 3.6410−0.3457 0.7394 3.6410 −0.3237 0.6820 3.6410 −0.3006 0.6221 3.6410−0.2764 0.5597 3.6410 −0.2511 0.4949 3.6410 −0.2246 0.4277 3.6410−0.1968 0.3581 3.6410 −0.1678 0.2862 3.6410 −0.1375 0.2118 3.6410−0.1068 0.1377 3.6410 −0.0758 0.0636 3.6410 −0.0445 −0.0102 3.6410−0.0129 −0.0840 3.6410 0.0191 −0.1576 3.6410 0.0514 −0.2311 3.64100.0837 −0.3045 3.6410 0.1158 −0.3781 3.6410 0.1478 −0.4517 3.6410 0.1795−0.5254 3.6410 0.2112 −0.5991 3.6410 0.2418 −0.6704 3.6410 0.2715−0.7392 3.6410 0.3002 −0.8054 3.6410 0.3281 −0.8691 3.6410 0.3552−0.9303 3.6410 0.3815 −0.9888 3.6410 0.4070 −1.0448 3.6410 0.4306−1.0958 3.6410 0.4523 −1.1418 3.6410 0.4719 −1.1828 3.6410 0.4895−1.2189 3.6410 0.5050 −1.2500 3.6410 0.5183 −1.2763 3.6410 0.5300−1.2986 3.6410 0.5399 −1.3172 3.6410 0.5482 −1.3325 3.6410 0.5549−1.3447 3.6410 0.5601 −1.3541 3.6410 0.5613 −1.3620 3.6410 0.5594−1.3685 3.6410 0.5561 −1.3728 3.6410 0.5528 −1.3753 3.6410 0.5491−1.3769 3.6410 0.5437 −1.3776 3.6410 0.5371 −1.3760 3.6410 0.5308−1.3709 3.6410 0.5250 −1.3617 3.6410 0.5175 −1.3498 3.6410 0.5081−1.3349 3.6410 0.4966 −1.3168 3.6410 0.4828 −1.2954 3.6410 0.4666−1.2704 3.6410 0.4473 −1.2409 3.6410 0.4250 −1.2069 3.6410 0.3996−1.1684 3.6410 0.3714 −1.1253 3.6410 0.3405 −1.0776 3.6410 0.3067−1.0252 3.6410 0.2719 −0.9702 3.6410 0.2361 −0.9127 3.6410 0.1993−0.8527 3.6410 0.1618 −0.7900 3.6410 0.1237 −0.7247 3.6410 0.0851−0.6566 3.6410 0.0462 −0.5856 3.6410 0.0087 −0.5139 3.6410 −0.0274−0.4415 3.6410 −0.0620 −0.3685 3.6410 −0.0953 −0.2947 3.6410 −0.1275−0.2205 3.6410 −0.1588 −0.1458 3.6410 −0.1892 −0.0706 3.6410 −0.21890.0049 3.6410 −0.2477 0.0808 3.6410 −0.2756 0.1571 3.6410 −0.3027 0.23383.6410 −0.3280 0.3081 3.6410 −0.3516 0.3803 3.6410 −0.3735 0.4501 3.6410−0.3939 0.5175 3.6410 −0.4128 0.5826 3.6410 −0.4302 0.6452 3.6410−0.4462 0.7055 3.6410 −0.4608 0.7633 3.6410 −0.4734 0.8160 3.6410−0.4841 0.8636 3.6410 −0.4931 0.9060 3.6410 −0.5009 0.9459 3.6410−0.5069 0.9806 3.6410 −0.5103 1.0075 3.6410 −0.5113 1.0292 3.6410−0.5105 1.0454 3.6410 −0.5082 1.0574 3.6410 −0.5055 1.0636 3.6410−0.5028 1.0670 3.6410 −0.5010 1.0682 3.6410 −0.5000 1.0687 3.6410−0.4842 1.1170 3.7690 −0.4836 1.1171 3.7690 −0.4826 1.1172 3.7690−0.4804 1.1169 3.7690 −0.4764 1.1152 3.7690 −0.4711 1.1109 3.7690−0.4633 1.1015 3.7690 −0.4548 1.0877 3.7690 −0.4453 1.0684 3.7690−0.4350 1.0435 3.7690 −0.4227 1.0107 3.7690 −0.4088 0.9728 3.7690−0.3943 0.9322 3.7690 −0.3781 0.8865 3.7690 −0.3601 0.8357 3.7690−0.3403 0.7798 3.7690 −0.3195 0.7214 3.7690 −0.2976 0.6606 3.7690−0.2747 0.5972 3.7690 −0.2507 0.5314 3.7690 −0.2254 0.4632 3.7690−0.1988 0.3926 3.7690 −0.1709 0.3196 3.7690 −0.1417 0.2443 3.7690−0.1120 0.1691 3.7690 −0.0820 0.0941 3.7690 −0.0515 0.0193 3.7690−0.0206 −0.0554 3.7690 0.0107 −0.1299 3.7690 0.0425 −0.2042 3.76900.0744 −0.2784 3.7690 0.1062 −0.3527 3.7690 0.1379 −0.4270 3.7690 0.1693−0.5014 3.7690 0.2006 −0.5759 3.7690 0.2308 −0.6479 3.7690 0.2602−0.7174 3.7690 0.2887 −0.7843 3.7690 0.3164 −0.8486 3.7690 0.3433−0.9103 3.7690 0.3695 −0.9695 3.7690 0.3949 −1.0259 3.7690 0.4185−1.0774 3.7690 0.4401 −1.1237 3.7690 0.4598 −1.1651 3.7690 0.4774−1.2015 3.7690 0.4929 −1.2329 3.7690 0.5063 −1.2593 3.7690 0.5180−1.2818 3.7690 0.5280 −1.3005 3.7690 0.5363 −1.3159 3.7690 0.5431−1.3282 3.7690 0.5483 −1.3376 3.7690 0.5497 −1.3456 3.7690 0.5478−1.3522 3.7690 0.5445 −1.3565 3.7690 0.5412 −1.3590 3.7690 0.5374−1.3606 3.7690 0.5320 −1.3612 3.7690 0.5254 −1.3596 3.7690 0.5191−1.3543 3.7690 0.5133 −1.3451 3.7690 0.5056 −1.3331 3.7690 0.4961−1.3181 3.7690 0.4844 −1.2999 3.7690 0.4705 −1.2784 3.7690 0.4541−1.2532 3.7690 0.4345 −1.2235 3.7690 0.4118 −1.1894 3.7690 0.3861−1.1507 3.7690 0.3576 −1.1072 3.7690 0.3263 −1.0591 3.7690 0.2923−1.0062 3.7690 0.2573 −0.9508 3.7690 0.2213 −0.8928 3.7690 0.1846−0.8322 3.7690 0.1473 −0.7688 3.7690 0.1094 −0.7027 3.7690 0.0711−0.6337 3.7690 0.0328 −0.5618 3.7690 −0.0040 −0.4892 3.7690 −0.0394−0.4158 3.7690 −0.0732 −0.3417 3.7690 −0.1056 −0.2669 3.7690 −0.1370−0.1915 3.7690 −0.1673 −0.1157 3.7690 −0.1968 −0.0395 3.7690 −0.22530.0372 3.7690 −0.2529 0.1143 3.7690 −0.2796 0.1919 3.7690 −0.3052 0.26983.7690 −0.3291 0.3453 3.7690 −0.3512 0.4186 3.7690 −0.3716 0.4895 3.7690−0.3906 0.5580 3.7690 −0.4079 0.6241 3.7690 −0.4238 0.6878 3.7690−0.4384 0.7489 3.7690 −0.4515 0.8076 3.7690 −0.4628 0.8611 3.7690−0.4723 0.9094 3.7690 −0.4802 0.9524 3.7690 −0.4870 0.9928 3.7690−0.4923 1.0280 3.7690 −0.4953 1.0552 3.7690 −0.4962 1.0770 3.7690−0.4953 1.0934 3.7690 −0.4929 1.1054 3.7690 −0.4902 1.1117 3.7690−0.4875 1.1151 3.7690 −0.4857 1.1164 3.7690 −0.4847 1.1168 3.7690−0.4686 1.1677 3.8980 −0.4681 1.1678 3.8980 −0.4670 1.1679 3.8980−0.4648 1.1675 3.8980 −0.4609 1.1654 3.8980 −0.4560 1.1607 3.8980−0.4488 1.1507 3.8980 −0.4412 1.1362 3.8980 −0.4327 1.1163 3.8980−0.4235 1.0907 3.8980 −0.4122 1.0573 3.8980 −0.3994 1.0186 3.8980−0.3858 0.9773 3.8980 −0.3706 0.9309 3.8980 −0.3536 0.8793 3.8980−0.3351 0.8225 3.8980 −0.3156 0.7632 3.8980 −0.2950 0.7013 3.8980−0.2733 0.6370 3.8980 −0.2505 0.5702 3.8980 −0.2264 0.5009 3.8980−0.2010 0.4293 3.8980 −0.1743 0.3552 3.8980 −0.1462 0.2788 3.8980−0.1175 0.2025 3.8980 −0.0884 0.1265 3.8980 −0.0587 0.0506 3.8980−0.0286 −0.0251 3.8980 0.0021 −0.1005 3.8980 0.0333 −0.1758 3.89800.0649 −0.2509 3.8980 0.0964 −0.3260 3.8980 0.1278 −0.4012 3.8980 0.1589−0.4765 3.8980 0.1898 −0.5518 3.8980 0.2198 −0.6246 3.8980 0.2489−0.6949 3.8980 0.2772 −0.7625 3.8980 0.3047 −0.8275 3.8980 0.3315−0.8899 3.8980 0.3576 −0.9496 3.8980 0.3829 −1.0067 3.8980 0.4065−1.0586 3.8980 0.4281 −1.1054 3.8980 0.4478 −1.1472 3.8980 0.4655−1.1839 3.8980 0.4810 −1.2156 3.8980 0.4945 −1.2422 3.8980 0.5062−1.2649 3.8980 0.5163 −1.2839 3.8980 0.5247 −1.2994 3.8980 0.5315−1.3117 3.8980 0.5368 −1.3213 3.8980 0.5381 −1.3293 3.8980 0.5363−1.3359 3.8980 0.5331 −1.3404 3.8980 0.5298 −1.3429 3.8980 0.5260−1.3445 3.8980 0.5204 −1.3451 3.8980 0.5137 −1.3433 3.8980 0.5074−1.3379 3.8980 0.5015 −1.3286 3.8980 0.4938 −1.3164 3.8980 0.4841−1.3013 3.8980 0.4722 −1.2829 3.8980 0.4580 −1.2610 3.8980 0.4413−1.2356 3.8980 0.4214 −1.2056 3.8980 0.3983 −1.1710 3.8980 0.3723−1.1318 3.8980 0.3433 −1.0879 3.8980 0.3116 −1.0391 3.8980 0.2772−0.9855 3.8980 0.2419 −0.9293 3.8980 0.2056 −0.8703 3.8980 0.1687−0.8085 3.8980 0.1312 −0.7440 3.8980 0.0934 −0.6767 3.8980 0.0554−0.6065 3.8980 0.0176 −0.5333 3.8980 −0.0187 −0.4594 3.8980 −0.0533−0.3849 3.8980 −0.0862 −0.3098 3.8980 −0.1177 −0.2340 3.8980 −0.1480−0.1578 3.8980 −0.1773 −0.0812 3.8980 −0.2055 −0.0042 3.8980 −0.23270.0733 3.8980 −0.2589 0.1512 3.8980 −0.2840 0.2294 3.8980 −0.3080 0.30823.8980 −0.3302 0.3846 3.8980 −0.3508 0.4589 3.8980 −0.3697 0.5308 3.8980−0.3870 0.6004 3.8980 −0.4029 0.6676 3.8980 −0.4172 0.7323 3.8980−0.4303 0.7945 3.8980 −0.4420 0.8541 3.8980 −0.4521 0.9085 3.8980−0.4606 0.9574 3.8980 −0.4675 1.0011 3.8980 −0.4734 1.0421 3.8980−0.4778 1.0778 3.8980 −0.4803 1.1053 3.8980 −0.4809 1.1274 3.8980−0.4798 1.1439 3.8980 −0.4773 1.1561 3.8980 −0.4747 1.1624 3.8980−0.4720 1.1659 3.8980 −0.4702 1.1672 3.8980 −0.4692 1.1676 3.8980

In the exemplary embodiments, as embodied by the invention, for examplethe stage compressor vane, there are many airfoils, which are un-cooled.For reference purposes only, there is established point-0 passingthrough the intersection of the airfoil and the platform along thestacking axis.

It will also be appreciated that the exemplary airfoil(s) disclosed inthe above TABLE A may be scaled up or down geometrically for use inother similar compressor designs. Consequently, the coordinate valuesset forth in TABLE A may be scaled upwardly or downwardly such TABLE Athe airfoil profile shape remains unchanged. A scaled version of thecoordinates in the TABLE A would be represented by X, Y and Z coordinatevalues of the TABLE A multiplied or divided by a constant.

In particular, as embodied by the invention, the airfoil as defined byTABLE A, can be applied in a compressor of a turbine, for example, butnot limited to, as General Electric “7FA+c” compressor. Moreover, thevane airfoil profile, as embodied by the invention, can comprise a Stage4 rotor vane of a compressor. This compressor is merely illustrative ofthe intended applications for the airfoil, as embodied by the invention.Moreover, it is envisioned that the airfoil of TABLE A, as embodied bythe invention, can also be used as rotor vanes in GE Frame F-classturbines, as well as GE's Frame 6 and 9 turbines, given the scaling ofthe airfoil, as embodied by the invention.

The airfoils impart kinetic energy to the airflow and therefore bringabout a desired flow across the compressor. The airfoils turn the fluidflow, slow the fluid flow velocity (in the respective airfoil frame ofreference), and yield a rise in the static pressure of the fluid flow.The configuration of the airfoil (along with its interaction withsurrounding airfoils), as embodied by the invention, including itsperipheral surface provides for stage airflow efficiency, enhancedaeromechanics, smooth laminar flow from stage to stage, reduced thermalstresses, enhanced interrelation of the stages to effectively pass theairflow from stage to stage, and reduced mechanical stresses, amongother desirable aspects of the invention. Typically, multiple rows ofairfoil stages, such as, but not limited to, rotor/rotor airfoils, arestacked to achieve a desired discharge to inlet pressure ratio. Airfoilscan be secured to wheels or a case by an appropriate attachmentconfiguration, often known as a “root”, “base” or “dovetail”.

The configuration of the airfoil and any interaction with surroundingairfoils, as embodied by the invention, that provide the desirableaspects fluid flow dynamics and laminar flow of the invention can bedetermined by various means. Fluid flow from a preceding/upstreamairfoil intersects with the airfoil, as embodied by the invention, andvia the configuration of the instant airfoil, flow over and around theairfoil, as embodied by the invention, is enhanced. In particular, thefluid dynamics and laminar flow from the airfoil, as embodied by theinvention, is enhanced. There is a smooth transition fluid flow from anypreceding/upstream airfoil(s) and a smooth transition fluid flow to theadjacent/downstream airfoil(s). Moreover, the flow from the airfoil, asembodied by the invention, proceeds to the adjacent/downstreamairfoil(s) is enhanced due to the enhanced laminar fluid flow off of theairfoil, as embodied by the invention. Therefore, the configuration ofthe airfoil, as embodied by the invention, assists in the prevention ofturbulent fluid flow in the unit comprising the airfoil, as embodied bythe invention.

For example, but in no way limiting of the invention, the airfoilconfiguration (with or without fluid flow interaction) can be determinedby computational modeling, Fluid Dynamics (CFD); traditional fluiddynamics analysis; Euler and Navier-Stokes equations; for transferfunctions, algorithms, manufacturing: manual positioning, flow testing(for example in wind tunnels), and modification of the airfoil; in-situtesting; modeling: application of scientific principles to design ordevelop the airfoils, machines, apparatus, or manufacturing processes;airfoil flow testing and modification; combinations thereof, and otherdesign processes and practices. These methods of determination aremerely exemplary, and are not intended to limit the invention in anymanner.

As noted above, the airfoil configuration (along with its interactionwith surrounding airfoils), as embodied by the invention, including itsperipheral surface provides for stage airflow efficiency, enhancedaeromechanics, smooth laminar flow from stage to stage, reduced thermalstresses, enhanced interrelation of the stages to effectively pass theairflow from stage to stage, and reduced mechanical stresses, amongother desirable aspects of the invention, compared to other similarairfoils, which have like applications. Of course, other such advantagesare within the scope of the invention.

While various embodiments are described herein, it will be appreciatedfrom the specification that various combinations of elements, variationsor improvements therein may be made by those skilled in the art, and arewithin the scope of the invention.

What is claimed is:
 1. An article of manufacture, the article having anominal profile substantially in accordance with Cartesian coordinatevalues of X, Y and Z set forth in TABLE A, and wherein X and Y aredistances in inches which, when connected by smooth continuing arcs,define airfoil profile sections at each distance Z in inches, theprofile sections at the Z distances being joined smoothly with oneanother to form a complete airfoil shape.
 2. An article of manufactureaccording to claim 1, wherein the airfoil shape comprises an airfoil. 3.An article of manufacture according to claim 2, wherein said airfoilshape lies in an envelope within ±0.160 inches in a direction normal toany article surface location.
 4. An article of manufacture according toclaim 1, wherein the airfoil shape comprises a rotor vane.
 5. Acompressor comprising a compressor wheel having a plurality of blades,each of said blades cooperating with a plurality of rotor vanes, theplurality of rotor vanes comprising an airfoil having an airfoil shape,said airfoil shape having a nominal profile substantially in accordancewith Cartesian coordinate values of X, Y and Z set forth in TABLE A,wherein X and Y are distances in inches which, when connected by smoothcontinuing arcs, define the airfoil profile sections at each distance Zin inches, the profile sections at the Z distances being joined smoothlywith one another to form a complete airfoil shape.
 6. A compressorcomprising a compressor wheel having a plurality of blades, each of saidblades cooperating with a plurality of rotor vanes, the plurality ofrotor vanes comprising an airfoil having an uncoated nominal airfoilprofile substantially in accordance with Cartesian coordinate values ofX, Y and Z set forth in TABLE A, wherein X and Y are distances in incheswhich, when connected by smooth continuing arcs, define airfoil profilesections at each distance Z in inches, the profile sections at the Zdistances being joined smoothly with one another to form a completeairfoil shape, the X and Y distances being scalable as a function of thesame constant or number to provide at least one of a scaled up vaneairfoil and scaled down vane airfoil.
 7. A compressor according to claim6 wherein the plurality of rotor vanes comprise a Stage 4 rotor vane. 8.A compressor according to claim 6 wherein said airfoil shape lies in anenvelope within ±0.160 inches in a direction normal to any airfoilsurface location.